Inductive proximity detectors are already known in the trade, which supply a signal when a metal member passes in the vicinity of the head. These detectors operate on an on/off basis, i.e. the resonant circuit oscillates in the absence of a metal member to be detected, the oscillation being interrupted upon the presence of a metal member in its vicinity, which has the effect of greatly increasing the apparent resistance of the inductance of the circuit, i.e. of causing a great reduction in the coefficient .OMEGA.=.omega.L/R. However, in practice it is not possible to use a detector of this type for detecting a strand travelling rapidly in front of the detection head, owing to the very small diameter of this strand. The signal obtained is insufficiently defined and it may also be confused with the parasite signals.